A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters;

Question

2 years ago

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A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters;

for example, ABIK is a different code from BAIK. )
The size of the sample space is 1.)_________
A.120 B.360 C.840 D.1680
. The probability that the first three letters of the four-letter code are vowels is 2.)_________.
A.1/35 B.1/60 C.1/140 D.101/105

Mathematics

1 answer:

oksano4ka [1.4K] · Answer 1 · 2022-07-07T08:40:58+03:00

To answer this question, use permutation since the order of the letter matters. There are 7 letters and only 4 are to be used for the code. This is a permutation of 7 taken 4 (7P4) which is equal to 840. Thus, the sample space is 840.
For the next questions, there are 3 vowels for as the first letter, only 6 letters are available for the second, 5 on the next, and 4 on the last. Multiplying these numbers give 360. To solve for probability, divide this number with the sample space. Thus, the answer is 3/7.